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Incompressible finite element methods for Navier-Stokes equations with nonstandard boundary conditions in $ {\bf R}\sp 3$


Author: V. Girault
Journal: Math. Comp. 51 (1988), 55-74
MSC: Primary 65N30; Secondary 76-08, 76D05
DOI: https://doi.org/10.1090/S0025-5718-1988-0942143-2
MathSciNet review: 942143
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Abstract: This paper is devoted to the steady state, incompressible Navier-Stokes equations with nonstandard boundary conditions of the form $ {\mathbf{u}} \cdot {\mathbf{n}} = 0$, $ \mathbf{curl}\;{\mathbf{u}} \times {\mathbf{n}} = {\mathbf{0}}$, either on the entire boundary or mixed with the standard boundary condition $ {\mathbf{u}} = {\mathbf{0}}$ on part of the boundary. The problem is expressed in terms of vector potential, vorticity and pressure. The vorticity and vector potential are approximated with curl-conforming finite elements and the pressure with standard continuous finite elements. The error estimates yield nearly optimal results for the purely nonstandard problem.


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DOI: https://doi.org/10.1090/S0025-5718-1988-0942143-2
Article copyright: © Copyright 1988 American Mathematical Society